This open access book bridges a gap between introductory Quantum Field Theory (QFT) courses and state-of-the-art research in scattering amplitudes. It covers the path from basic definitions of QFT to amplitudes, which are relevant for processes in the Standard Model of particle physics. The book begins with a concise yet self-contained introduction to QFT, including perturbative quantum gravity. It then presents modern methods for calculating scattering amplitudes, focusing on tree-level amplitudes, loop-level integrands and loop integration techniques. These methods help to reveal intriguing relations between gauge and gravity amplitudes and are of increasing importance for obtaining high-precision predictions for collider experiments, such as those at the Large Hadron Collider, as well as for foundational mathematical physics studies in QFT, including recent applications to gravitational wave physics.These course-tested lecture notes include numerous exercises with solutions. Requiring only minimal knowledge of QFT, they are well-suited for MSc and PhD students as a preparation for research projects in theoretical particle physics. They can be used as a one-semester graduate level course, or as a self-study guide for researchers interested in fundamental aspects of quantum field theory.
At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum field theory. Bridging the gap between introductory courses on quantum field theory and state-of-the-art research, these concise yet self-contained and course-tested lecture notes are well-suited for a one-semester graduate level course or as a self-study guide for anyone interested in fundamental aspects of quantum field theory and its applications. The numerous exercises and solutions included will help readers to embrace and apply the material present ed in the main text.
How are firms, networks of firms, and production systems organized and how does this organization vary from place to place? What are the new geographies emerging from the need to create, access, and share knowledge, and sustain competitiveness? In what ways are local clusters and global exchange relations intertwined and co-constituted? What are the impacts of global changes in technology, demand, and competition on the organization of production, and how do these effects vary between communities, regions, and nations? This book synthesizes theories from across the social sciences with empirical research and case studies in order to answer these questions and to demonstrate how people and firms organize economic action and interaction across local, national, and global flows of knowledge and innovation. It is structured in four clear parts: - Part I: Foundations of Relational Thinking - Part II: Relational Clusters of Knowledge - Part III: Knowledge Circulation Across Territories - Part IV: Toward a Relational Economic Policy? The book employs a novel relational framework, which recognizes values, interpretative frameworks, and decision-making practices as subject to the contextuality of the social institutions that characterize the relationships between the human agents. It will be a valuable resource for academics, researchers, and graduate students across the social sciences, and practitioners in clusters policy.
The right to self-determination is renowned for its lack of clear interpretation. Broadly speaking, one can differentiate between a 'classic' and a 'romantic' tradition. In modern international law, the balance between these two opposing traditions is sought in an attempt to contain or 'domesticate' the romantic version by limiting it to 'abnormal' situations, that is cases of 'alien subjugation, domination and exploitation'. This book situates Russia's engagement with the right to self-determination in this debate. It shows that Russia follows a distinct approach to self-determination that diverges significantly from the consensus view in international state practice and scholarship, partly due to a lasting legacy of the former Soviet doctrine of international law. Against the background of the Soviet Union's role in the evolution of the right to self-determination, the bulk of the study analyses Russia's relevant state practice in the post-Soviet space through the prisms of sovereignty, secession, and annexation. Drawing on analysis of all seven major secessionist conflicts in the former Soviet space and a detailed study of Russian sources and scholarship, it traces how Russian engagement with self-determination has changed over the past three decades. Ultimately, the book argues that Russia's approach to the right of peoples to self-determination should not only be understood in terms of power politics disguised as legal rhetoric but in terms of a continuously assumed regional hegemony and exceptionalism, based on balance-of-power considerations.
In less than a decade, activism against the fossil fuel industry has exploded across the globe. While environmentalists used to focus on legislative goals, such as carbon emissions trading or renewable energy policies, today the most prominent activists directly attack the fossil fuel industry. This timely book offers a comprehensive evaluation of different types of activism, the success and impact of campaigns and activities, and suggestions as to ways forward. This book is the first systematic treatment of the anti-fossil fuel movement in the United States. An accessible and readable text, it is an essential reference for scholars, policymakers, activists, and citizens interested in climate change, fossil fuels, and environmental sustainability. The entire book or chapters from it can be used as required or supplementary material in various courses at the undergraduate and graduate level. As the book is not technically challenging but contains a comprehensive review of climate change, fossil fuels, and the literature on environmental activism, it can be used as an accessible introduction to the anti-fossil fuel campaign across disciplines.
These songs are a source of endless delight." — Grove's Dictionary. One hundred and twenty songs that complete the Brahms song oeuvre: Wie Melodien zieht es and 18 other songs of Opp. 105, 106, 107, 121; 10 additional songs; and sensitive arrangements of 91 folk and traditional songs. English translations.
Despite their long tradition spices are subject to international modern scientific research. This has made it necessary to disseminate knowledge to a large audience of interest. The book addresses this need by informing the reader about the complex worldwide use of spice plants. The many spice and aromatic plants are arranged in alphabetical order of their botanical relevance. It includes all species which have been cultivated for the above purposes. It also covers species whose usage has long ceased or which are used only rarely or have become wild. In this respect the author has aimed at comprehensiveness. In total over 1400 plants have been collated. The very extensive register of literature has been designed to facilitate intensive study of a specific plant or spice. Works both on botany and agriculture, and on chemistry, pharmacodynamics and usage have been considered. The book is aimed principally at spice and aroma experts, pharmacists, botanists and interested lay persons. But the author also had in mind food chemists, dieticians and agricultural scientists, for whom botany, chemistry and pharmacological aspects may be of interest. It is hoped that those occupied in the spice and aroma industry involved in creating spice blends and the like will also take inspiration from the book.
The first comprehensive book in more than a century to reveal the diversity and natural history of diving beetles. Among the hundreds of thousands of species of beetles, there is one family, containing some 4,300 species, that stands out as one of the most diverse and important groups of aquatic predatory insects. This is the Dytiscidae, whose species are commonly known as diving beetles. No comprehensive treatment of this group has been compiled in over 130 years, a period during which a great many changes in classification and a near quadrupling of known species has occurred. In Diving Beetles of the World, Kelly B. Miller and Johannes Bergsten provide the only full treatments of all 188 Dytiscid genera ever assembled. Entomologists, systematists, limnologists, ecologists, and others with an interest in aquatic systems or insect diversity will find these extensively illustrated keys and taxon accounts immensely helpful. The keys make it possible to identify all taxa from subfamily to genera, and each key and taxon treatment is accompanied by both photographs and detailed pen-and-ink drawings of diagnostic features. Every genus account covers body length, diagnostic characters, classification, species diversity, a review of known natural history, and world distribution. Each account is also accompanied by a range map and at least one high-resolution habitus image of a specimen. Diving beetles are fast becoming important models for aquatic ecology, world biogeography, population ecology, and animal sexual evolution and, with this book, the diversity of the group is finally accessible.
This book explores legal and constitutional issues in Hong Kong's relationship with mainland China through an analysis of the litigation on the right of abode of the children of Hong Kong residents who are born and live in the mainland. The litigation in the Hong Kong courts and the subsequent interpretation by the Standing Committee of the National People's Congress were followed with keen interest both locally and internationally, and had provoked great controversy. The differing approaches to and styles of interpretation of the Court and the Standing Committee provide a vivid demonstration of the clash of legal systems within which Hong Kong's constitutional system has to operate. These issues are discussed in this book by Hong Kong's leading legal scholars and practitioners. This book offers perspectives to solve these controversies and to develop an acceptable approach to the interpretation of the Basic Law. It captures the sustained public debate on constitutional issues and provides a historical record of this constitutional debate. It also contains the full texts of the decision of the Court and the Interpretation by the Standing Committee.
Urban development and housing projects in Berlin and Naples in the post-war era – A comparison: Theoretical models, implemented projects, social and political impacts today
Urban development and housing projects in Berlin and Naples in the post-war era – A comparison: Theoretical models, implemented projects, social and political impacts today
In the post-war period, Berlin and Naples experienced a phase of profound changes, essentially influenced by external factors: the less rigid urban structure which had been ruined by World War II, resulting in severe changes in the social and economic structure, an uncritical reception and implementation of largely theoretical models of functionalism in urban planning, and in the design of the new public building interventions. On the one hand, between the 1940s and the 1980s, Berlin experienced a considerable loss in population, a political isolation and an urban splitting, as the urban planning institutions, deeply influenced by relevant politics, slowly and thoroughly changed the cityscape. On the other hand, Naples suffered from a new phase of immigration as well as from the parallel densification of the old suburbs and the physical expansion of the city limits without consistent and socially appropriate urban planning measures. This phase of change, so full of contrasts, coincided with the establishment of new democratic systems in the Federal Republic of Germany and Italy, and with the fundamental goal of socially adequate housing in both the West and the East. The research involved a series of historical analyses of the relationship between urban development and social housing for critical reflection and to allow an informed evaluation of the contemporary condition. In particular, it investigated housing settlements realised in Berlin and Naples in the first four decades of the post-war period, which corresponds to the period in which public housing was central in both political and urban planning terms. The book focuses on places of living, the city and the house. Consequently, it investigates the scale of the project and that of the intervention, the relationship between innovation and the cultural reception of urban phenomena and, again, between the stage of the project and the realisation and upkeep of the interventions, between democratic expectations and the adequacy of the administration system. These steps have a direct effect on the social identity that inspires, structures and transforms the planned and then built city, that continuous dialogue between form and content (the past) that occurs, in general, through progressive and mutual adaptations. In the selection of the case studies, we have favoured interventions on the “periphery,” which are those in which theoretical and aesthetic trends have best manifested themselves and in which planning and design cultures could develop most widely. However, the periphery does not necessarily coincide with the geographical edges of the cities: both in Berlin and in Naples, historical events, or the particular topography have naturally shifted the “peripheral” location along a radius that only ideally starts from the city centre and often extends to its inner fringes. Rather, from a sociological point of view, the same interventions generally generate the peripheral condition, that is, marginalisation or social division. This, as we shall see, can be traced both on the large scale of the city and inside the neighbourhood. The materials are arranged in the following way: the text is introduced by a graphic and synthetic presentation of the historical context in Berlin and Naples and the documentation of the twelve case studies. In the second chapter, Comparison, which was mostly developed as the first by the young scholars involved in the project, three theoretical issues highlighted during the seminars are better presented: The ability of the project to involve the social level; the experimentalism of the interventions, in particular in construction technology, social approach and democratic participation; the relationship between public and private in the phases of implementation and the upkeep of the programmes. The third chapter, In-Depth Analysis, includes the contributions of the scientists involved to give a better articulated historical and critical analysis of many of selected case studies and of the wider urban and social context. The closing editorial paper offers a brief overview focusing on a selection of the theoretical nodes that emerged from the comparison of the materials from a contemporary perspective. The publication is the outcome of the homonymous research programme fully funded by DAAD German Academic Exchange Service and runned in 2019 in cooperation between the Technische Universität of Berlin, Department of Architecture (Habitat Unit) with the Università della Campania "Luigi Vanvitelli," Dipartimento di Architettura e Disegno Industriale in Aversa (Italy). In der Nachkriegszeit erlebten Berlin und Neapel eine Phase tiefgehender Veränderungen, die im Wesentlichen von externen Faktoren beeinflusst wurde: der aufgelockerten, infolge des Zweiten Weltkriegs ruinierten Stadtform, der starken Veränderung der sozialen und wirtschaftlichen Struktur, der unkritischen Rezeption und Implementierung von stark theoretisch geprägten Modellen des Funktionalismus in der Stadtplanung sowie in der Gestaltung der neuen öffentlichen Bauinterventionen. Auf der einen Seite erlebt Berlin zwischen den 40er und den 80er Jahren einen starken Bevölkerungsverlust, eine politische Isolierung und eine urbane Aufspaltung, indem eine stark politisch beeinflusste Stadtplanung das Stadtbild tief verändert. Auf der anderen Seite leidet Neapel unter einer neuen Einwanderungsphase sowie der parallelen Verdichtung der alten Vorstädte und der physischen Erweiterung der Stadtgrenze, ohne dass konsequente und sozial gemäße stadtplanerische Maßnahmen vorgenommen wurden. Diese kontrastreiche Umbruchsphase stimmt überein mit der Etablierung der neuen demokratischen Regierungssysteme in der Bundesrepublik Deutschland wie auch in Italien und damit mit dem für beide - und im Westen wie im Osten - grundlegenden Ziel des sozial gerechten Wohnens. Das Forschungsvorhaben beinhaltete eine Reihe von historischen Analysen der Beziehung zwischen Stadtentwicklung und sozialem Wohnungsbau zum Zweck der kritischen Reflexion und um eine fundierte Bewertung der jeweiligen zeitgenössischen Bedingungen zu ermöglichen. Insbesondere wurden Wohnsiedlungen untersucht, die in Berlin wie in Neapel in den ersten vier Jahrzehnten nach dem Zweiten Weltkrieg errichtet wurden, d.h. in eben dem Zeitraum, in dem öffentlicher Wohnungsbau sowohl unter politischen wie auch unter stadtplanerischen Aspekten zentral war. Das Buch konzentriert sich auf Lebensräume, die Stadt und das Haus. Folglich untersucht es das Ausmaß des Projekts wie das der Intervention, die Beziehung zwischen Innovation und kultureller Rezeption städtischer Phänomene wie auch zwischen dem jeweiligen Stadium des Projekts und der Umsetzung und Aufrechterhaltung der Interventionen und schließlich zwischen den demokratischen Erwartungen und der Leistungsfähigkeit des Verwaltungssystems. Diese Schritte haben direkte Auswirkungen auf die soziale Identität, welche die zunächst geplante und dann gebaute Stadt inspiriert, strukturiert und transformiert, d.h. diesen ständigen Dialog zwischen Form und Inhalt (die Vergangenheit), der im Allgemeinen durch fortschreitende und gegenseitige Anpassungen abläuft. Bei der Auswahl der Fallstudien haben wir Interventionen in der "Perpherie" bevorzugt, da sie es sind, in denen sich theoretische und ästhetische Trends am deutlichsten abzeichnen und in denen sich Kulturen der Planung und des Designs am weitesten entwickeln könnten. Die Peripherie fällt jedoch nicht unbedingt zusammen mit den geografischen Rändern der Städte: sowohl in Berlin wie in Neapel haben historische Ereignisse oder auch die jeweilige Topografie naturgemäß die "periphere" Lage entlang einem Radius verschoben, der nur im Idealfall vom Stadtzentrum ausgeht und sich oft bis an seine Ränder erstreckt. Von einer soziologischen Perspektive aus ist es eher so, dass im Allgemeinen die gleichen Interventionen zu einer peripheren Situation führen. d.h. zu Marginalisierung oder sozialer Aufspaltung. Wie wir sehen werden, gilt dies sowohl im größeren Rahmen für die Stadt wie auch innerhalb eines Stadtviertels. Die Materialien sind folgendermaßen angeordnet: Der Text wird eingeführt durch eine grafische und zusammenfassende Präsentation der historischen Zusammenhänge in Berlin und Neapel und eine Dokumentation zu den zwölf Fallstudien. Im zweiten Kapitel – "Vergleich/Comparison" – , das ursprünglich als erstes Kapitel von den jüngeren Forschern, die am Projekt teilnahmen, entwickelt wurde, werden drei Fragen, die während der Seminare im Mittelpunkt standen, genauer vorgestellt: die Eignung des Projekts dafür, die soziale Ebene mit einzubeziehen; der experimentelle Charakter der Interventionen, insbesondere in der Bautechnologie, im sozialen Ansatz und in der demokratischen Teilhabe; die Beziehung zwischen öffentlichem und privatem Engagement in der Phase der Umsetzung wie der Aufrechterhaltung der Programme. Das dritte Kapitel – "Eingehende Analyse/In-Depth-Analyses" – besteht aus den Beiträgen der beteiligten Wissenschaftler, um so eine klarere historische und kritische Analyse von etlichen der ausgewählten Fallstudien und der weiterreichenden städtischen und sozialen Zusammenhänge zu gewährleisten. Der abschließende Kommentarteil bietet einen kurzen Überblick, der den Schwerpunkt auf eine Auswahl von theoretischen Verknüpfungen legt, die sich aus dem Vergleich der Materialien aus zeitgenössischen Perspektive ergeben. Die Veröffentlichung ist das Ergebnis des gleichnamigen Forschungsprogramms, das vollständig vom DAAD (Deutscher Akademischer Austauschdienst) finanziert wurde und 2019 in einer Zusammenarbeit der Architektur-Fakultät (Habitat Unit) der Technischen Universität Berlin mit dem Dipartmento di Architettura e Disegno Industriale der Università della Campania "Luigi Vanvitelli" in Aversa (Italien) durchgeführt wurde. Nel secondo dopoguerra Berlino e Napoli vivono una fase di profondo cambiamento che è condizionato in maniera preponderante da fattori esterni: la parziale disgregazione della forma urbana causata dei bombardamenti bellici, il cambiamento della struttura socio-economica, il recepimento delle teorie funzionaliste nella pianificazione urbana e nella progettazione dei nuovi interventi di edilizia residenziale pubblica. Per un verso, tra gli anni quaranta e gli anni ottanta, Berlino rileva una pesante contrazione demografica, l'isolamento politico, la separazione interna del Muro, gli effetti di una pianificazione urbana fortemente influenzata dal sdoppiato piano politico che deriva dalla fondazione nel 1949 dei due stati tedeschi, la GDR e la DDR. Per altro verso, Napoli osserva una nuova fase di immigrazione che si aggiunge alla naturale crescita demografica del primo dopoguerra, lo sviluppo urbano dei sobborghi e dei principali centri dell’entroterra costiero, l'espansione fisica ma non amministrativa dei confini della città, l’inadeguatezza ed il costante ritardo del piano amministrativo-urbanistico nella gestione dei fenomeni sociali ed urbani. Si tratta in pratica di una fase carica di contrasti che coincide con l'instaurazione delle nuove repubbliche liberali in Germania ed Italia, e con la definitiva affermazione della questione abitativa e della residenza popolare che assurge, in ambito socialista, al rango di elemento funzionale alla stessa costruzione statale. Lo studio indaga la relazione tra sviluppo urbano ed edilizia residenziale pubblica e si propone come strumento per la riflessione critica e per la valutazione informata della condizione contemporanea. Le indagini e le valutazioni storiche che esso raccoglie si concentrano sugli interventi realizzati a Berlino e a Napoli nei primi quarant’anni del dopoguerra, ovvero nel periodo in cui la questione abitativa diviene urgente e centrale per vari ordini di motivi sia in termini politici che urbanistici. Lo sguardo si concentra sui luoghi dell'abitare, la città e la casa; indaga e confronta la scala teorica e quella reale, il rapporto tra innovazione e recezione culturale; confronta i piani del progetto, della costruzione e della successiva manutenzione degli interventi residenziali, tra le aspettative democratiche e l'adeguatezza del sistema amministrativo nel gestirli. Si tratta di passaggi che hanno un effetto diretto sull'identità sociale che, di risposta, ispira e struttura la nuova città attraverso un dialogo tra forma e contenuto (il passato) che procede per progressivi e reciproci adattamenti. Nella selezione dei casi studio sono stati privilegiati interventi di "periferia", ovvero quelli in cui le culture della pianificazione e del progetto, e le tendenze teoriche ed estetiche si sono potute manifestare nella maniera più completa. Come si vedrà, tuttavia, la periferia non coincide necessariamente con i margini geografici delle città: sia a Berlino che a Napoli gli eventi storici o la particolare topografia hanno dislocato la condizione "periferica" lungo un raggio che solo idealmente conduce dal centro della città. Da un punto di vista sociologico, e per la coincidenza di diversi fattori, inoltre, gli stessi interventi residenziali generano al loro interno la condizione periferica che si manifesta generalmente in degrado degli spazi comuni, mancanza di prossimità, emarginazione sociale. I materiali del testo sono organizzati in tre parti: nel primo capitolo Documentation si introduce al contesto storico, amministrativo ed urbanistico e si presentano schematicamente e secondo un criterio uniforme i dodici casi studio selezionati; nel secondo capitolo Comparison, che, come il primo, è stato redatto dai giovani ricercatori coinvolti nel progetto di ricerca, vengono meglio presentate tre questioni teoriche emerse nel corso dei laboratori: la capacità del progetto di coinvolgere il piano sociale; lo sperimentalismo degli interventi, in particolare per tecnologia costruttiva, approccio sociale e partecipazione democratica; il rapporto tra il piano amministrativo-pubblico ed il piano civico-privato nelle fasi di realizzazione e mantenimento dei programmi residenziali. Il terzo capitolo, In-Depth-Analysis, raccoglie i contributi degli studiosi coinvolti per fornire un'analisi storica e critica articolata dei casi di studio selezionati e del più ampio contesto urbano e sociale. Infine, le conclusioni raccolgono e presentano i principali nodi teorici emersi nel corso della ricerca in una prospettiva aperta alla condizione contemporanea. La pubblicazione restituisce e meglio sviluppa sul piano documentale e critico i materiali raccolti nel corso dei due laboratori tenuti nel 2019 presso la Technische Universität di Berlino, Dipartimento di Urbanistica e Sviluppo urbano sostenibile “Habitat Unit,” e l’Università della Campania "Luigi Vanvitelli," Dipartimento di Architettura e Disegno Industriale di Aversa, nell’ambito dell’omonimo progetto di ricerca finanziato dal DAAD (Servizio Tedesco per lo Scambio Accademico).
Since the 1980s, scientists have been researching adaptive structures for materials, for multifunctional elements or even for complete systems. Adaptronics (smart materials, smart structures, smart systems) is a field of distinct interdisciplinarity. The book therefore offers an interdisciplinary view of adaptronic systems, materials and functional elements and their applications. The subject matter integrates various engineering disciplines, from electrical engineering and information technology to manufacturing and control engineering, materials engineering and structural mechanics - to name but a few of the relevant subject areas. Starting from the basic principles and variants of adaptronic systems and functional materials, the textbook explains the different construction methods of functional elements. Building on this, readers learn how to apply this knowledge to active shape control, active vibration control and active vibroacoustics. For each of these topics the author presents current examples from research, discusses research results and future research questions. Each of the nine chapters closes with references to further literature. An index of the mathematical symbols used and a keyword index facilitate learning for readers.The book is aimed at Master's students in engineering courses such as mechanical engineering, aerospace engineering, mechatronics, automotive engineering and related courses. The book provides a comprehensive overview for industrial practitioners who want to familiarize themselves with the field of adaptronics and also serves as a reliable reference book.
In vector optimization one investigates optimal elements such as min imal, strongly minimal, properly minimal or weakly minimal elements of a nonempty subset of a partially ordered linear space. The prob lem of determining at least one of these optimal elements, if they exist at all, is also called a vector optimization problem. Problems of this type can be found not only in mathematics but also in engineer ing and economics. Vector optimization problems arise, for exam ple, in functional analysis (the Hahn-Banach theorem, the lemma of Bishop-Phelps, Ekeland's variational principle), multiobjective pro gramming, multi-criteria decision making, statistics (Bayes solutions, theory of tests, minimal covariance matrices), approximation theory (location theory, simultaneous approximation, solution of boundary value problems) and cooperative game theory (cooperative n player differential games and, as a special case, optimal control problems). In the last decade vector optimization has been extended to problems with set-valued maps. This new field of research, called set optimiza tion, seems to have important applications to variational inequalities and optimization problems with multivalued data. The roots of vector optimization go back to F. Y. Edgeworth (1881) and V. Pareto (1896) who has already given the definition of the standard optimality concept in multiobjective optimization. But in mathematics this branch of optimization has started with the leg endary paper of H. W. Kuhn and A. W. Tucker (1951). Since about v Vl Preface the end of the 60's research is intensively made in vector optimization.
This open access book bridges a gap between introductory Quantum Field Theory (QFT) courses and state-of-the-art research in scattering amplitudes. It covers the path from basic definitions of QFT to amplitudes, which are relevant for processes in the Standard Model of particle physics. The book begins with a concise yet self-contained introduction to QFT, including perturbative quantum gravity. It then presents modern methods for calculating scattering amplitudes, focusing on tree-level amplitudes, loop-level integrands and loop integration techniques. These methods help to reveal intriguing relations between gauge and gravity amplitudes and are of increasing importance for obtaining high-precision predictions for collider experiments, such as those at the Large Hadron Collider, as well as for foundational mathematical physics studies in QFT, including recent applications to gravitational wave physics.These course-tested lecture notes include numerous exercises with solutions. Requiring only minimal knowledge of QFT, they are well-suited for MSc and PhD students as a preparation for research projects in theoretical particle physics. They can be used as a one-semester graduate level course, or as a self-study guide for researchers interested in fundamental aspects of quantum field theory.
At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum field theory. Bridging the gap between introductory courses on quantum field theory and state-of-the-art research, these concise yet self-contained and course-tested lecture notes are well-suited for a one-semester graduate level course or as a self-study guide for anyone interested in fundamental aspects of quantum field theory and its applications. The numerous exercises and solutions included will help readers to embrace and apply the material present ed in the main text.
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